Reptation of a chain

Figure 5 The basic concept of P.G. De Gennes reptation of a chain trapped in a tube-like region by migration of "defects" along the nhain.

To understand this viscosity enhancement, it is easier to start with the theory for linear polymers. The behavior of linear polymers can be described by the reptation model.For a linear polymer of high molecular weight in the melt, chains can be modeled as a confined tube where the diffusion of the chain is restricted along the tube contour. Entanglements are formed between chains where the reptation of a chain along its contour becomes the dominant mode of movement. The addition of a branch point prevents reptation and other forms of movement must occur for the chain to change its configuration. In the case... 

Figure 8 Reptation of a chain within a tube. (A test chain [black] reptates through a tube with walls formed by segments of the chains [gray]).

Here c is a geometrical constant ( 15 for 5 = 2) and N is the average number of entanglements per chain in the pre-crosslinked state T is the relaxation time (by reptation) of a chain in this state. As the gel point is approached, the longest relaxation time does not diverge, according this treatment, but approaches a constant value... 

Figure C2.1.13. (a) Schematic representation of an entangled polymer melt, (b) Restriction of tire lateral motion of a particular chain by tire otlier chains. The entanglement points tliat restrict tire motion of a chain define a temporary tube along which tire chain reptates.

Figure 8.11. Reptation of a polymer chain. The chain moves snake-like through its confining...

Fig. 18. Mean square displacement of a chain segment undergoing reptational motion as a function of time...

Fig. 19a-c. Schematic representation of a reptating chain in different time regimes a Short-time unrestricted Rouse motion b equilibration of density fluctuations along tha chain c creep motion of a chain out of its tube. 

In order to calculate the effects of CLF we have to ask how the fraction of monomers that is released through CLF at the chain ends grows with time. It has been recently shown that for Ktr the effect of reptation on escaping from the tube is negligible in comparison to CLF [90]. It is the first passage of a chain end that is assumed to relax the constraint of a tube segment on a chain. From the scale invariance of the Rouse equation (Eq. 3.7) an exact asymptotic result... 

DeGennes,P.G. Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys. 55,572-579 (1971). 

In a celebrated series of papers, Doi and Edwards [80] used the reptation, or tube model, to develop a theory for the rheological properties of entangled chains. In this model, the dynamics of a chain is described by the tube of entanglements. The configuration of the... 

Figure 6. Relative relaxation of a chain-end in PS DH 184 ( ) with estimated error bars, compared to the prediction of fluctuation, retraction and reptation...

The stress relaxation modulus G t) for the reptation model was calculated by Doi and Edwards in 1978 by solving the first-passage problem for the diffusion of a chain in a tube (see Problem 9.6) ... 

The simple reptation model does not properly account for all the relaxation modes of a chain confined in a tube. This manifests itself in all measures of terminal dynamics, as the longest relaxation time, diffusion coefficient and viscosity all have stronger molar mass dependences than the reptation model predicts. Tn Sections 9.4.5 and 9.6.2, more accurate ana-... 

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